Problem session #5
SCENARIO: Suppose you are interested in learning about the determinants of demand for
packs of cigarettes (per month) by young adult smokers between the ages of 18 and 30. An
elected official with ties to the tobacco industry has claimed that falling real incomes in a mild
recession that is likely to result from global economic instability will have a large negative effect
on cigarette consumption by this group. Being aware of the commonly addictive properties of
nicotine, you wish to determine the effect of a decrease in income on cigarette consumption.
You have collected a random sample of 30 young adults and have recorded their ages (AGEi
in years), incomes (INCi in thousands of dollars), the price they typically pay for a pack of
cigarettes (PRICEi in dollars), and the average number of packs per month they smoke
(PACKSi per month). The statistical analyses you perform are given in the Exhibits #6.
a.
Based on Regression 1, what is the verbal interpretation of the slope? Test the
hypothesis that a $1,000 decrease in annual income (recession) will have no effect on
the number of packs of cigarettes consumed per month by smokers in this age group
b.
Based upon the simple regression results the Regression 1, do cigarettes appear to
be inferior (as opposed to normal) goods? Explain how you have reached this
conclusion.
c.
Based on Regression 1, what level of monthly cigarette consumption is expected for a
smoker with a monthly income of $50,000? Give the formula for a point estimate and
explain explicitly BUT DO NOT CALCULATE how a 95% confidence interval for this
prediction would be constructed
You finally remember that demand functions are functions of several variables, not just one at
a time. You estimate Regression 2 in order to ascertain the effects of both income and price
on the number of packs of cigarettes consumed per month.
d.
Controlling for income levels do cigarette prices have any statistically discernible effect
on cigarette consumption?
e.
What will be the expected effect of a $0.50 additional tax on each pack of cigarettes?
f.
What is the interpretation of the intercept term in Regression 2? Should you be interest
in testing statistical hypotheses about the magnitude of the intercept in this model? Why
or why not? Explain.
g.
Determine the adjusted r-squared for regression 2
h.
According to Regression 3, is a recession likely to improve health outcomes by causing
a statistically significant decrease in monthly cigarette consumption?
i.
According to Regression 3, should we be concerned about the effect of prices on packs
j.
For Regression 3, test the hypothesis that none of the explanatory variables has any
effect on the dependent variable. Explain your reasoning.
k.
Test the hypothesis that the economic variables, price and income, are not jointly
significant in explaining the dependent variable packs.
Q.2
Textbook, page 181, question 6.5
Q.3
Given the model Log Yi = 0 + 1D1+ 2D2 + 3 Log X3 + i
Where
Yi = income in corporate America
D1= is a dummy variable for gender = 1 if Female
D2 = is a dummy variable for race = 1 if Black
X3 = Motivation
You obtained the following estimated regression model
Log Yi = 10 - .098D1 - .079D2 + 2.7 Log X3
a.
b.
Interpret all three coefficients including the intercept term
What sucks more, being black or female? Explain
Q.4
Suppose you are estimating a wage equation in which an individual’s wage is explained as function of
their experience, skills, race gender etc.
Using experience as the only productivity measure, you obtained the following model:
WAGE   0  1 EXP   2 RACE   3 SEX  
Race =1 if white, 0 otherwise and Sex = 1 if male and 0 otherwise.
Find:
a. Expected wage for a non-white male.
b. How would you test if there’s a difference in the expected wages of a non white male and a
nonwhite female?
c. What about between a nonwhite male and a white female?